Abstract: We consider learning the structures of Gaussian latent tree models with
vector observations when a subset of them are arbitrarily corrupted. First, we
present the sample complexities of Recursive Grouping (RG) and Chow-Liu
Recursive Grouping (CLRG) without the assumption that the effective depth is
bounded in the number of observed nodes, significantly generalizing the results
in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly
reduces the sample complexity of RG from being exponential in the diameter of
the tree to only logarithmic in the diameter for the hidden Markov model (HMM).
Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by
using the truncated inner product. These robustified algorithms can tolerate a
number of corruptions up to the square root of the number of clean samples.
Finally, we derive the first known instance-dependent impossibility result for
structure learning of latent trees. The optimalities of the robust version of
CLRG and NJ are verified by comparing their sample complexities and the